Optical burst switching (OBS) is emerging as one promising switching paradigm for the next generation optical networks. To support multiple services in burst-switching networks, the OBS paradigm should support some quality-of-service (QoS) provisioning. A major design issue in such networks is to reduce the blocking probability of the bursts arising due to resource contention at the intermediate core router. In this paper, we propose a signaling protocol which we call ‘Delay-on-Demand’ (OBS-DoD), to reduce blocking probability and support QoS in optical burst-switching networks. The proposed scheme guarantees that at least one of the bursts succeeds depending on its priority, propagation delay from the ingress router, and the burst-size when contention occurs at the core router. For this, we use a control packet to delay, in case of a contention, the transmission of bursts at the ingress router. We compare the performance of our proposal, by simulation, with an earlier proposed scheme, and show that the proposed OBS-DoD outperforms the earlier scheme in reducing the blocking probability. For simulation, we generated bursty traffic using an M/Pareto distribution.